Slater–Pauling rule

Application

The use of the rule depends on carefully defining what it means for an electron to lie outside of the d shell. The electrons outside a d shell are the electrons which have higher energy than the electrons within the d shell. The Madelung rule (incorrectly) suggests that the s shell is filled before the d shell. For example, it predicts Zinc has a configuration of [Ar] 4s² 3d¹⁰. However, Zinc's 4s electrons actually have more energy than the 3d electrons, putting them outside the d shell. Ordered in terms of energy, the electron configuration of Zinc is [Ar] 3d¹⁰ 4s². (see: the n+ℓ energy ordering rule)

The basic rule given above makes several approximations. One simplification is rounding to the nearest integer. Because we are describing the number of electrons in a band using an average value, the s and d shells can be filled to non-integer numbers of electrons, allowing the Slater–Pauling rule to give more accurate predictions. While the Slater–Pauling rule has many exceptions, it is often a useful as an approximation to more accurate, but more complicated physical models.

Building on further theoretical developments done by physicists such as Jacques Friedel, a more widely applicable version of the rule, known as the generalized Slater–Pauling rule was developed.